Air-Conditioning Assembly

ABSTRACT

The invention relates to a motor vehicle air-conditioning assembly provided with a supercritical fluid refrigerant circuit and comprising a pressure relief member ( 12 ) defining a cross-section of fluid flow. The assembly comprises an electronic control device ( 401 ) for interacting with the fluid refrigerant circuit. The electronic control device includes a computing function using an estimation of the cross-section of flow of the pressure relief member, the density coefficient of the fluid refrigerant, and the pressure of the fluid refrigerant at the inlet of the pressure relief member for calculating an estimation of the mass flow rate of the fluid refrigerant in the pressure relief member ( 12 ).

The invention relates to motor vehicle air conditioning circuits.

In conventional motor vehicles, the compressor of the air conditioningcircuit is driven by the engine and therefore consumes part of theengine's power. The power absorbed by the compressor, when it isoperating, reduces the efficiency of the engine and consequentlyincreases the fuel consumption and the pollution generated by theexhaust gases from the vehicle. This drawback is problematic in the caseof mechanical compressors with an external control, the use of which iscommonplace.

Moreover, in existing constructions, the fuel injection computer of thevehicle does not have the instantaneous value of the actual powerabsorbed by the compressor and therefore chooses, for the operation ofthe compressor, fuel injection parameters by default, which correspondto the maximum value of the power absorbed, which value is rarelyreached in practice.

Consequently, one solution for optimizing the efficiency of the engineconsists in estimating the instantaneous value of this power actuallyabsorbed by the compressor. When this information is known, it is thenpossible to adapt the fuel injection parameters of the engine to theactual requirements.

In existing constructions, an estimate of the refrigerant mass flow rateis used to calculate the instantaneous power absorbed by the compressor.

Such constructions generally involving subcritical refrigerants areunsuitable for supercritical refrigerants.

The use of supercritical refrigerants, especially the CO₂ refrigerantR744, was developed for vehicle air conditioning circuits in order tolimit the deleterious effects of refrigerants on the environment. TheCO₂ refrigerant has a much smaller global warming effect thansubcritical refrigerants, such as the HFC refrigerants of the R134atype.

An air conditioning circuit using a supercritical fluid comprises acompressor, a gas cooler, an internal heat exchanger, an expander and anevaporator, the refrigerant passing through these in the above order. Insuch a circuit, the cooling of the refrigerant after compressionundergoes no phase change. The refrigerant passes into the liquid stateonly during the expansion. This property of supercritical fluids meansthat the assembly given in patent application 01/16568 cannot be used toestimate the supercritical refrigerant flow rate and the power consumedby the compressor.

US 2003/0115896 A1 proposes an air conditioning unit for estimating themass flow rate of a supercritical refrigerant, based on a measurement ofthe high pressure and a measurement of the low pressure. However, inorder for the estimate for the mass flow rate to be sufficientlyaccurate, it is necessary for the air conditioning circuit to becontrolled so that the refrigerant leaving the expander is almostentirely in the liquid state. Moreover, a sensor is required formeasuring the low pressure, which increases the cost of the airconditioning unit.

French patent application 03/03362 also proposes an air conditioningunit for estimating the mass flow rate of a supercritical refrigerant.To do this, the proposed air conditioning unit includes a calculatingfunction that uses two differences in temperature relating to the gascooler, at least one of which is based on the temperature of therefrigerant at a chosen intermediate point on the gas cooler. Thisintermediate point is in particular located at a distance x_(i) from theinlet of the gas cooler that is between 5% and 35% of the total lengthof the gas cooler. However, this assembly requires a large number ofsensors (sensors for measuring the refrigerant pressure at the inlet andoutlet of the compressor, the temperature of the refrigerant at theinlet of the gas cooler, the temperature of the stream of air receivedby the gas cooler and the temperature of the refrigerant at the chosenintermediate point on the gas cooler), which therefore increases thecost of the assembly.

The subject of the present invention is an air conditioning unit thatremedies these known drawbacks of the prior art.

For this purpose, the invention proposes a motor vehicle airconditioning unit, provided with a supercritical refrigerant circuitcomprising a compressor, a gas cooler, an expander, defining arefrigerant flow area, and an evaporator. The assembly further includesan electronic control device designed to interact with the refrigerantcircuit. Advantageously, the electronic control device includes acalculating function using an estimate of the flow area of the expander,the density of the refrigerant and the pressure of the refrigerant atthe inlet of the expander in order to calculate an estimate of therefrigerant mass flow rate at the expander.

According to one aspect of the invention, the flow area of the expanderis estimated from the refrigerant pressure at the inlet of the expander.

In particular, the electronic control device may be capable of reactingto the fact that the value of the refrigerant pressure P₂₀ at the inletof the expander is:

-   -   less than or equal to a first pressure value P1, a first        constant S1 being assigned to the flow area of the expander;    -   less than or equal to a second pressure value P2 greater than        the first pressure value P1, by solving the following equation        in order to calculate an estimate of the flow area S of the        expander:        S=S1+(S2−S1)×(P ₂₀ −P1)/(P2−P1),    -   where S2 is a second constant;    -   less than or equal to a third pressure value P3 and greater than        the second pressure value P2, solving the following equation in        order to calculate an estimate of the flow area S of the        expander:        S=S2+(S3−S2)×(P ₂₀ −P2)/(P3−P2),    -   where S3 is a third constant; and    -   greater than or equal to the third pressure value P3, a fourth        constant S4 being assigned to the flow area of the expander.

In one particular embodiment, the first pressure value P1 isapproximately equal to 80 bar, the second pressure value P2 isapproximately equal to 110 bar and the third pressure value P3 isapproximately equal to 135 bar, while the first constant S1 isapproximately equal to 0.07 mm², the second constant S2 is approximatelyequal to 0.5 mm², the third constant S3 is approximately equal to 0.78mm² and the fourth constant S4 is approximately equal to 3.14 mm².

According to another aspect of the invention, the calculating functionis specific to calculating the density of the refrigerant from therefrigerant temperature at the inlet of the expander and from therefrigerant pressure at the inlet of the expander.

The air conditioning unit may include a probe placed at the inlet of theexpander for measuring the refrigerant temperature at the inlet of theexpander.

The air conditioning unit may also include a sensor placed at the inletof the expander for measuring the refrigerant pressure at the inlet ofthe expander.

As a complement, the electronic control device may include a powerestimation function capable of estimating the power absorbed by thecompressor from:

-   -   the refrigerant mass flow rate provided by the calculating        function;    -   the work of the compressor; and    -   the rotation speed of the compressor.

The electronic control device is capable of estimating the work of thecompressor from the refrigerant pressure at the inlet of the expander,from the refrigerant pressure at the inlet of the compressor and from arefrigerant temperature relative to the compressor.

Advantageously, the refrigerant pressure at the inlet of the compressoris estimated from a pressure at the inlet or at the outlet of theevaporator combined with the refrigerant mass flow rate.

Furthermore, the pressure at the inlet or at the outlet of theevaporator is determined from the refrigerant temperature, saidtemperature being either measured by a probe or estimated from:

-   -   a temperature relative to the evaporator;    -   the efficiency of the evaporator; and    -   the temperature of the air to be cooled.

The refrigerant temperature relative to the compressor may be therefrigerant temperature at the inlet of the compressor.

The air conditioning unit may then include a probe placed at the inletof the compressor for measuring the refrigerant temperature at the inletof the compressor.

As a variant, the refrigerant temperature relative to the compressor maybe the refrigerant temperature at the outlet of the compressor.

The air conditioning installation may then include a probe placed at theoutlet of the compressor for measuring the refrigerant temperature atthe outlet of the compressor.

The invention also covers a product-program, which may be defined ascomprising the functions used for estimating the refrigerant mass flowrate and the power consumed by the compressor.

Other features and advantages of the invention will become apparent onexamining the detailed description below and the appended drawings inwhich:

FIG. 1A is a diagram of a motor vehicle air conditioning circuitoperating with a supercritical refrigerant;

FIG. 1B is a diagram of an air conditioning unit according to theinvention;

FIG. 2 is a plot showing the variations in the flow area of the expanderas a function of the refrigerant pressure at the inlet of the expander;

FIG. 3 is a flow diagram showing the steps implemented by the controldevice for estimating the refrigerant mass flow rate at the expander;

FIG. 4 is a flow diagram showing the steps implemented by the controldevice for estimating the flow area of the expander;

FIG. 5 is a flow diagram representing the steps implemented by thecontrol device for estimating the power consumed by the compressor,according to the invention;

FIGS. 6 and 7 are diagrams of the air conditioning circuit according toalternative embodiments of the invention;

FIGS. 8 to 12 are schematic diagrams showing the position of thetemperature probes used for determining the pressure at the inlet or atthe outlet of the evaporator;

FIG. 13 illustrates the method of determining the pressure of therefrigerant at the inlet of the compressor; and

FIG. 14 shows the relationship between the refrigerant mass flow rateand the refrigerant pressure at the inlet of the compressor.

Appendix A comprises the main mathematical equations used forimplementing the assembly.

The drawings essentially contain elements having a certain character.They therefore serve not only for making the description more clearlyunderstood but also for contributing to the definition of the invention,where appropriate.

FIG. 1A represents an air conditioning circuit through which asupercritical refrigerant flows. Hereafter, the description will referto the supercritical refrigerant CO₂ as a nonlimiting example.

Such a circuit conventionally comprises:

-   -   a compressor 14 suitable for receiving the refrigerant in the        gaseous state and compressing it;    -   a gas cooler 11 suitable for cooling the gas compressed by the        compressor;    -   an expander 12 suitable for lowering the pressure of the        refrigerant; and    -   an evaporator 13 suitable for making the refrigerant from the        expander pass from the liquid state to the gaseous state in        order to produce a stream of conditioned air 21 that is sent        into the passenger compartment of the vehicle.

The circuit may further include an internal heat exchanger 23, allowingthe refrigerant flowing from the gas cooler to the expander to give upheat to the refrigerant flowing from the evaporator to the compressor.The circuit may further include an accumulator 17 placed between theoutlet of the evaporator and the inlet of the compressor, in order toavoid liquid surges.

The gas cooler 11 receives a stream of external air 16 for extractingthe heat taken from the passenger compartment, which stream undercertain operating conditions is blown by a motor/fan unit 15.

The evaporator 13 receives a stream of air from a blower, in order toproduce a stream of conditioned air 21.

The expander 12 may have a variable flow area, such as an electronicexpander, a thermostatic expander or any other expander for which theflow area depends on the high pressure. The expander 12 may also have afixed flow area, such as a calibrated orifice.

The supercritical refrigerant is compressed in the gaseous phase andraised to a high pressure by the compressor 14. The gas cooler 11 thencools the refrigerant by means of the incoming stream of air 16. Unlikethe air conditioning circuits operating with a subcritical refrigerant,the cooling of the refrigerant after compression does not involve aphase change. The refrigerant passes to the two-phase state, with avapor content that depends on the low pressure, only during theexpansion. The internal heat exchanger 23 allows the refrigerant to bevery strongly cooled.

Referring now to FIG. 1B, this shows an air conditioning unit accordingto the invention installed in a motor vehicle.

The motor vehicle is driven by an engine 43, which may be controlled bya fuel injection computer 42. The fuel injection computer 42 receivesinformation from various sensors, which it interprets in order to adjustthe injection parameters.

The fuel injection computer 42 may also provide information about theconditions inside or outside the vehicle (information provided by asolar sensor, number of occupants, etc.). In particular, it may provideinformation about instantaneous values relating to the operation of thevehicle, and especially about the rotational speed N of the compressor.

The unit is also provided with an air conditioning computer 40,comprising a passenger compartment regulator 41 and an air conditioningloop regulator 402. The passenger compartment regulator 41 is designedto set the temperature setpoint of the external air blown into theevaporator 13.

The engine fuel injection computer may act on the air conditioning unitvia an air conditioning regulator 402. This link may prevent theoperation of the air conditioning unit when the engine is on high load.

The air conditioning unit according to the invention is based on a modelof the expander, in order to provide an estimate of the refrigerant massflow rate m_(exp) at the expander.

The air conditioning unit includes an electronic control device, forexample an electronic card 401, designed to interact with the airconditioning circuit 10 via the links 30/31 and with the fuel injectioncomputer 42 via the links 32/33.

The electronic card 401 may be considered as an integral part of thevehicle air conditioning computer 40.

The electronic card 401 may receive information 30 coming from sensorsfitted on the air conditioning circuit 10. It may also receiveinformation from the engine fuel injection computer 42 via the link 33,in particular the rotation speed N of the compressor and/or the runspeed V of the vehicle.

The Applicant has found that the expander may be modelled by equationA10 of Appendix A, where K is a coefficient that characterizes theexpander, in particular its pressure drop.

From this model, the calculating function can calculate an estimate ofthe refrigerant mass flow rate m_(exp) at the expander from:

-   -   the pressure P₂₀ of the refrigerant at the inlet of the        expander;    -   the density ρ of the CO₂ refrigerant; and    -   the flow area S (in mm²) of the expander.

The Applicant has also found that the density ρ of the CO₂ refrigerantmay be estimated from the temperature T₃₀ at the inlet of the expanderand from the pressure P₂₀ at the inlet of the expander, according toequation A11 of Appendix A.

The Applicant has furthermore found that the flow area S (in mm²) of anexpander with a flow area depends on the refrigerant pressure P₂₀ at theinlet of the expander.

Thus, an estimate of the refrigerant mass flow rate m_(exp) at theexpander may be obtained from the refrigerant pressure P₂₀ at the inletof the expander and from the temperature T₃₀ at the inlet of theexpander.

The refrigerant pressure P₂₀ at the inlet of the expander and therefrigerant temperature T₃₀ at the inlet of the expander may beestimated or measured.

The air conditioning circuit may include two separate sensors formeasuring the refrigerant pressure P₂₀ at the inlet of the expander andthe refrigerant temperature T₃₀ at the inlet of the expander,respectively. As a variant, the air conditioning circuit may have asingle sensor placed at the inlet of the expander for measuring boththese quantities.

FIG. 2 is a plot showing the variation in the flow area S (in mm²) as afunction of the refrigerant pressure P₂₀ (in bar) at the inlet of theexpander. The curves shown on this plot correspond to equations A2 to A5of Appendix A.

As long as the refrigerant pressure P₂₀ at the inlet of the expander isless than or equal to a first pressure value P1, the area S is equal toa first constant S1 according to equation A2 of Appendix A.

When the pressure P₂₀ is above the first pressure value P1 and less thanor equal to a second pressure value P2, the area S follows a straightline whose directrix is determined from the values of S1, P1, P2 and asecond constant S2, in accordance with equation A3 of Appendix A. Thevalue of S2 corresponds to the value of the area S when P₂₀ is equal tothe valave P2.

When the pressure P₂₀ is greater than the second pressure value P2 andless than or equal to a third pressure value P3, the area S follows astraight line whose directrix is determined from the values of S2, P2,P3 and a third constant S3 in accordance with equation A4 of Appendix A.

When the pressure P₂₀ is greater than or equal to the third pressurevalue P3, the area S is equal to a fourth constant S4 greater than thethird constant S3 in accordance with equation A5 of Appendix A.

In particular, the first pressure value P1 may be approximately equal to80 bar, the second pressure value P2 may be approximately equal to 110bar, the third pressure value P3 may be approximately equal to 135 bar,the first constant S1 may be approximately equal to 0.07 mm², the secondconstant S2 may be approximately equal to 0.5 mm², the third constant S3may be approximately equal to 0.78 mm² and the fourth constant S4 may beapproximately equal to 3.14 mm².

As a complement, the estimate of the refrigerant mass flow rate,provided by the calculating function of the electronic card, may be usedto calculate the mechanical power absorbed. To do this, the electroniccard includes a power estimation function capable of estimating thepower P_(abs) absorbed by the compressor from the refrigerant mass flowrate m_(exp). In particular, the power estimation function is capable ofestimating the power P_(abs) absorbed by the compressor from theisentropic work of compression W_(ise) and from the rotation speed N ofthe compressor in accordance with equation A6 of Appendix A. Thecoefficients a and b are related to operating parameters of the airconditioning circuit. The coefficient a corresponds to the mechanicalefficiency relative to the isentropic compression of the compressor andis around 1.38. The coefficient b is the image of the compressorefficiency and corresponds to the friction factor of the compressor.

In accordance with equation A7 of Appendix A, the isentropic compressionpower W_(ise) is related:

-   -   to the refrigerant mass flow rate m_(exp), an estimate of which        is calculated by the calculating function as described above;        and    -   to the isentropic work ΔH_(ise) of the compressor.

The Applicant has found that the estimate of the work ΔH_(ise) of thecompressor may be obtained, in accordance with equation A80 of AppendixA, from:

-   -   the refrigerant pressure P₂₀ at the inlet of the expander;    -   the refrigerant pressure P₃₅ at the inlet of the compressor; and    -   the temperature of the refrigerant T_(comp) relative to the        compressor.

The refrigerant pressure P₃₅ at the inlet of the compressor and thetemperature of the refrigerant T_(comp) relative to the compressor maybe estimated or measured.

The pressure of the refrigerant at the inlet of the compressor isestimated using the refrigerant mass flow rate m_(exp) calculated aboveand from the pressure drop Δp between the inlet of the evaporator 13 andthe inlet of the compressor 14.

As a variant, this estimate of the refrigerant pressure at the inlet ofthe compressor may be determined using the refrigerant mass flow ratem_(exp) calculated above and from the pressure drop Δp between theoutlet of the evaporator 13 and the inlet of the compressor 14.

The example below is described in relation to the inlet pressure of theevaporator 13, but this example can be transposed in a similar mannerusing the pressure at the outlet of the evaporator 13.

This pressure drop Δp is calculated from formula A90 of Appendix A, inwhich:

-   -   P₅₀ is an estimate of the pressure at the inlet of the        evaporator;    -   P₃₅ is the estimate of the refrigerant pressure at the inlet of        the compressor.

It is also known that this pressure drop Δp may be determined fromformula A100 in which:

-   -   K is a pressure drop coefficient;    -   ρ is the density of the refrigerant; and    -   V_(co) ₂ is the speed of the refrigerant.

In accordance with equation A101 of Appendix A, the speed of therefrigerant V_(co) ₂ can be determined from:

-   -   the refrigerant mass flow rate m_(exp) determined by means of        equation A10;    -   the refrigerant density ρ; and    -   a constant S corresponding to the mean flow area and mean flow        length, combining both the linear pressure drop and the singular        pressure drop, experienced by the refrigerant. From the two        equations A90 and A100 it is possible to estimate the pressure        of the refrigerant at the inlet of the compressor, as        illustrated by equation A9.

Thus, the only unknown in this equation is the estimate of the pressureP₅₀ at the inlet of the evaporator.

It is known from the fluids saturation law, otherwise known as the fluidstate law, that the pressure P₅₀ at the inlet of the evaporator dependsdirectly on the saturation temperature T₅₀ at the inlet of theevaporator. Over the operating range of interest to us, this equationmay be represented in the form of a second-order polynomial.

This saturation temperature T₅₀ of the pressure refrigerant may bemeasured or estimated.

When it is estimated, equation A91 of Appendix A is used, in which:

-   -   T₄₀ is a datum relating to the evaporator temperature available        on many air conditioning units. This involves a CTN or CTP probe        placed on the evaporator, the main objective of which in the        prior art is to prevent the evaporator from icing up when the        compressor stops. This temperature T₄₀ corresponds to the        surface temperature of one of the walls of the evaporator 13        (for example at the recess of the inserts, as illustrated in        FIG. 12) or to the air temperature at the outlet of the        evaporator;    -   η_(evap) is the image of the evaporator efficiency, which can be        easily related to a function of the voltage U for the air blower        of the evaporator in the passenger compartment and the run speed        V of the vehicle, as expressed in equation A910 of Appendix A;        and    -   T₆₀ is the temperature of the air to be cooled by the air        conditioning unit. This temperature is estimated according to        the temperature inside the passenger compartment, the        temperature outside the passenger compartment, the voltage U for        the blower, the position of the recycling flap of the air        conditioning unit and the run speed V of the vehicle. This        function is expressed in equation A920 of Appendix A.

FIGS. 8 and 9 illustrate the possibility of measuring the saturationtemperature T₅₀ of the refrigerant at the inlet of the evaporator 13either by means of an intrusive or direct temperature probe 51, that isto say a probe directly bathed by the refrigerant (FIG. 7), or by anonintrusive or indirect probe 52, which measures the temperature of therefrigerant on the basis of the temperature of the tube that istransporting it (FIG. 8).

FIGS. 10 and 11 show the possibility of measuring the saturationtemperature T₅₀ of the refrigerant at the outlet of the evaporator 13using means identical to the temperature measurement envisaged at theinlet of the evaporator 13.

This method of determining the refrigerant pressure at the inlet of thecompressor is summarized in FIG. 13 in the form of a block diagram inwhich:

-   -   if the temperature T₅₀ at the inlet or at the outlet of the        evaporator is estimated, then the following are used:        -   the evaporator efficiency η_(evap) determined from the            information available about the vehicle, such as blower            voltage U and the run speed V of the vehicle,        -   these two items of information are used also to determine            the temperature T60 of the air to be cooled, combined with            the temperature inside the passenger compartment and the            external temperature and        -   the evaporator efficiency η_(evap), the temperature T₆₀ of            the air to be cooled and the surface temperature T₄₀ of the            evaporator are combined to estimate the temperature T₅₀ at            the inlet of the evaporator 13;    -   if the temperature T₅₀ is measured, a temperature probe 51 or 52        delivers the expected value;    -   the estimated or measured temperature T₅₀ is used to determine        the pressure P₅₀ according to the refrigerant saturation law;    -   this pressure P₅₀ at the inlet or the outlet of the evaporator        13, combined with the refrigerant pressure P₂₀ at the inlet of        the expander, with the density ρ of the CO₂ refrigerant and the        flow area S (in mm²) of the expander allows the refrigerant mass        flow rate to be determined; and    -   finally, the combination of this mass flow rate information with        the estimate of the pressure P₅₀ at the inlet of the evaporator        allows the refrigerant pressure P₃₅ at the inlet of the        compressor to be determined without using a specific sensor and        thus without increasing the cost of the air conditioning unit.

FIG. 14 illustrates the relationship between the refrigerant mass flowrate and the refrigerant pressure P₃₅ at the inlet of the compressor.The x-axis of this curve represents the mass flow rate m_(exp) inkilograms per hour and the y-axis of this curve illustrates the pressuredrop Δp in bar between the inlet or the outlet of the evaporator 13 andthe inlet of the compressor 14. It may be seen that an error of around30 kg in the estimate of the mass flow rate results in an error ofaround 2 bar in the determination of P₃₅. This error is minor comparedwith the absolute operating pressure values, which are often greaterthan 35 bar.

The refrigerant temperature relative to the compressor may be therefrigerant temperature T₃₅ at the inlet of the compressor, inaccordance with equation A81 of Appendix A. R is the perfect gasconstant and M corresponds to the molar mass of the refrigerant. Theratio R/M may especially be equal to 188.7.

As a variant, the refrigerant temperature relative to the compressor maybe the refrigerant temperature T₃₆ at the outlet of the compressor inaccordance with equation A82 of Appendix A.

FIG. 3 is a flow diagram showing the steps implemented by the electroniccard for estimating the refrigerant mass flow rate m_(exp) and the powerconsumed by the compressor.

At step 100, the refrigerant pressure P₂₀ at the inlet of the expanderis estimated/measured. Referring to FIGS. 1B, 6 and 7, the refrigerantpressure P₂₀ at the inlet of the expander may be measured by a sensor 20placed at the inlet of the expander. As a variant, the pressure P₂₀ ofthe refrigerant at the inlet of the expander may be estimated.

At step 102, the electronic card 401 estimates the flow area S of theexpander 12 from the measured/estimated refrigerant pressure value P₂₀at the inlet of the expander in accordance with equations A4 and A5 ofAppendix A.

Step 102 is shown in detail in the flow diagram of FIG. 4. Theelectronic card determines if the measured value of the refrigerantpressure P₂₀ at the inlet of the expander is:

-   -   less than or equal to the first pressure value P1 (step 1020),        in which case the flow area of the expander is equal to S1;    -   greater than the first constant P1 and less than or equal to the        second pressure value P2 (step 1021), in which case the flow        area of the expander is given by equation A3 of Appendix A as a        function of the pressure P₂₀ obtained at step 100;    -   greater than the second pressure value P2 and less than or equal        to the third pressure value P3 (step 1022), in which case the        flow area of the expander is given by equation A4 of Appendix A,        as a function of the pressure P₂₀ obtained at step 100; and    -   greater than or equal to the third pressure value P3 (step        1023), in which case the flow area of the expander is equal to        S4.

At step 103, the electronic card provides an estimate/measurement of thetemperature T₃₀ at the inlet of the expander. The unit may include atemperature sensor 30 for measuring the refrigerant temperature T₃₀ atthe inlet of the expander, as shown in FIGS. 1B, 6 and 7. As a variant,the unit may include a single sensor 20 for measuring both the pressureP₂₀ and the temperature T₃₀ of the refrigerant at the inlet of theexpander. The refrigerant temperature T₃₀ at the inlet of the expandermay also be estimated.

At step 104, the electronic card 401 estimates the density ρ of the CO₂refrigerant. The density ρ of the CO₂ refrigerant may be calculatedaccording to equation A11 of Appendix A from the refrigerant pressureP₂₀ at the inlet of the expander, obtained at step 100, and from therefrigerant temperature T₃₀ at the inlet of the expander, obtained atstep 103.

At step 105 of FIG. 3, the electronic card 401 can then calculate therefrigerant mass flow rate m_(exp) according to equation A3 of AppendixA, from:

-   -   the refrigerant pressure P₂₀ at the inlet of the expander,        estimated/measured at step 100;    -   the flow area S (in mm²) of the expander, estimated at step 102;        and    -   the density ρ of the CO₂ refrigerant, estimated at step 104.

As a complement, the estimate of the refrigerant mass flow rate m_(exp)at the expander may be used to calculate the power P_(abs) consumed bythe compressor.

FIG. 5 is a flow diagram showing the steps implemented by the electroniccard for calculating the power P_(abs) consumed by the compressor fromthe estimate of the refrigerant mass flow rate m_(exp) at the expander.The estimate of the power absorbed by the compressor may in particularrequire a prior estimate of the work ΔH_(ise) of the compressor, inaccordance with equations A6 and A7 of Appendix A.

At step 200, the electronic card calculates an estimate of the workΔH_(ise) of the compressor in accordance with equation A8 of Appendix Afrom:

-   -   the refrigerant pressure P₂₀ at the inlet of the expander;    -   the refrigerant pressure P₃₅ at the inlet of the compressor; and    -   the refrigerant temperature T_(comp) relative to the compressor.

When the refrigerant temperature relative to the compressor is therefrigerant temperature T₃₅ at the inlet of the compressor (inaccordance with equation A81 of Appendix A), it can be measured by aprobe 35 placed at the inlet of the compressor, as shown in FIGS. 1B and6.

When the refrigerant temperature relative to the compressor is therefrigerant temperature T₃₆ at the outlet of the compressor (inaccordance with equation A82 of Appendix A), it can be measured by aprobe 36 placed at the outlet of the compressor, as shown in FIG. 7.

The refrigerant pressure P₁₂ at the inlet of the compressor may beestimated or measured.

At step 202, the electronic card calculates the isentropic power W_(ise)from the refrigerant mass flow rate m_(exp) obtained at step 105 and thework ΔH_(ise) of the compressor obtained at step 200, in accordance withequation A7 of Appendix A.

At step 204, the electronic card calculates an estimate of the powerP_(abs) absorbed by the compressor, according to equation A6 of AppendixA, from the isentropic power W_(ise) obtained at step 202 and therotation speed N of the compressor.

The rotation speed N of the compressor is supplied to the electroniccard by the engine fuel injection computer 42 via the link 33, withreference to FIG. 1B.

The computer may use the estimated value of the actual power consumed bythe compressor to adjust the injection parameters, thereby making itpossible to reduce the fuel consumption.

The air conditioning unit according to the invention makes it possibleto obtain a satisfactory estimate of the refrigerant mass flow rate atthe expander. Furthermore, this unit does not use a low-pressure sensorto estimate the refrigerant mass flow rate at the expander, therebyallowing the total cost of the unit to be reduced.

Of course, the present invention is not limited to the embodimentsdescribed above. It encompasses all alternative embodiments that aperson skilled in the art might envision.

The present invention also covers the software code that it uses, mostparticularly when this is available on any medium that can be read by acomputer. The expression “medium that can be read by a computer” coversa storage medium, for example a magnetic or optical storage medium, andalso a transmission means, such as a digital or analog signal.

APPENDIX A

Supercritical Refrigerant Mass Flow Ratem _(exp) =KSρ ln(P ₂₀ +C)   (A10)ρ=f(T ₃₀ , P ₂₀)   (A11)

Flow Area S of the Expander

IF P₂₀≦P1:S=S1   (A2)

If P1<P₂₀≦P2:S=S1+(S2−S1)(P ₂₀ −P1)/(P2−P1)   (A3)

If P2<P₂₀≦P3:S=S2+(S3−S2)/(P ₂₀ −P2)/(P3−P2)   (A4)

If P₂₀≧P3:S=S4   (A5)

Power Consumed by the CompressorP _(abs) =aW _(ise) +bN   (A6)

Isentropic Power W_(ise)W_(ise)=m_(exp)ΔH_(ise)   (A7)

Work ΔH_(ise) of the CompressorΔH _(ise) =f(P ₂₀ , P ₃₅ , T ₃₅)   (A80)ΔH _(ise)=[(P ₂₀ /P ₃₅)^((k−1)/k)−1](T ₃₅+273.15)(R/M)/(k−1)   (A81)ΔH _(ise)=[1−(P ₂₀ /P ₃₅)^((1−k)/k)](T ₃₆+273.15)(R/M)/(k−1)   (A82)

Estimate of the Refrigerant Pressure P₃₅ at the Inlet of the CompressorΔp=P ₅₀ −P ₃₅   (A90)Δp=k ρvCo ₂/2   (A100)Vco ₂ =M _(exp)/(ρS)   (A101)P ₃₆ =P ₅₀ −M _(exp) K(2ρS ²)   (A9)T ₆₀=(T ₄₀−(1−η_(evap))T ₆₀)/η_(evap)   (A91)T₅₀=>P₆₀ R744 refrigerant saturation law

1. A motor vehicle air conditioning unit, provided with a supercriticalrefrigerant circuit (10) comprising a compressor (14), a gas cooler(11), an expander (12), defining a refrigerant flow area, and anevaporator (13), the assembly further including an electronic controldevice designed to interact with the refrigerant circuit, characterizedin that the electronic control device includes a calculating functionusing an estimate of the flow area of the expander, the density (ρ) ofthe refrigerant and the pressure (P₂₀) of the refrigerant at the inletof the expander in order to calculate an estimate of the refrigerantmass flow rate (m_(exp)) at the expander.
 2. The air conditioning unitas claimed in claim 1, characterized in that the flow area of theexpander is estimated from the value of the refrigerant pressure (P₂₀)at the inlet of the expander.
 3. The air conditioning unit as claimed inclaim 2, characterized in that the electronic control device is capableof reacting to the fact that the value of the refrigerant pressure P₂₀at the inlet of the expander is: less than or equal to a first pressurevalue P1, a first constant S1 being assigned to the flow area S of theexpander; less than or equal to a second pressure value P2 greater thanthe first pressure value P1, by solving the following equation in orderto calculate an estimate of the flow area S of the expander:S=S1+(S2−S1)×(P ₂₀ −P1)/(P2−P1), where S2 is a second constant; lessthan or equal to a third pressure value P3 less than or equal to a thirdpressure value P3 and greater than the second pressure value P2, solvingthe following equation in order to calculate an estimate of the flowarea S of the expander:S=S2+(S3−S2)×(P ₂₀ −P2)/(P3−P2), where S3 is a third constant; andgreater than or equal to the third pressure value P3, a fourth constantS4 being assigned to the flow area of the expander.
 4. The airconditioning unit as claimed in claim 3, characterized in that the firstpressure value P1 is approximately equal to 80 bar, the second pressurevalue P2 is approximately equal to 110 bar and the third pressure valueP3 is approximately equal to 135 bar and in that the first constant S1is approximately equal to 0.07 mm², the second constant S2 isapproximately equal to 0.5 mm², the third constant S3 is approximatelyequal to 0.78 mm² and the fourth constant S4 is approximately equal to3.14 mm².
 5. The air conditioning unit as claimed in one of thepreceding claims, characterized in that the calculating function isspecific to calculating the density (ρ) of the refrigerant from therefrigerant temperature (T₃₀) at the inlet of the expander and from therefrigerant pressure (P₂₀) at the inlet of the expander.
 6. The airconditioning unit as claimed in claim 5, characterized in that itincludes a probe (30) placed at the inlet of the expander (12) formeasuring the refrigerant temperature (T₃₀) at the inlet of theexpander.
 7. The air conditioning unit as claimed in one of thepreceding claims, characterized in that it includes a sensor (20) placedat the inlet of the expander (12) for measuring the refrigerant pressure(P₂₀) at the inlet of the expander.
 8. The air conditioning unit asclaimed in one of the preceding claims, characterized in that theelectronic control device further includes a power estimation functioncapable of estimating the power absorbed by the compressor from: therefrigerant mass flow rate (m_(exp)) provided by the calculatingfunction; the work (ΔHise) of the compressor; and the rotation speed (N)of the compressor.
 9. The air conditioning unit as claimed in claim 8,characterized in that the electronic control device is capable ofestimating the work (ΔHise) of the compressor from the refrigerantpressure (P₂₀) at the inlet of the expander, from the refrigerantpressure (P₃₅) at the inlet of the compressor and from a refrigeranttemperature (T_(comp)) relative to the compressor.
 10. The airconditioning unit as claimed in claim 9, characterized in that therefrigerant pressure (P₃₅) at the inlet of the compressor is estimatedfrom a pressure (P₅₀) at the inlet or at the outlet of the evaporator(13) combined with the refrigerant mass flow rate (m_(exp)).
 11. The airconditioning unit as claimed in claim 10, characterized in that thepressure (P₅₀) at the inlet or at the outlet of the evaporator (13) isdetermined from the refrigerant temperature (T₅₀) at the inlet or at theoutlet of the evaporator (13), said temperature being either measured bya probe or estimated from: a temperature (T₄₀) relative to theevaporator (13); the efficiency (η_(evap)) of the evaporator (13); andthe temperature (T₆₀) of the air to be cooled.
 12. The air conditioningunit as claimed in one of claims 9 to 11, characterized in that therefrigerant temperature relative to the compressor (10) is therefrigerant temperature (T₃₅) at the inlet of the compressor.
 13. Theair conditioning unit as claimed in claim 12, characterized in that itincludes a probe (35) placed at the inlet of the compressor (14) formeasuring the refrigerant temperature (T₃₅) at the inlet of thecompressor.
 14. The air conditioning unit as claimed in one of claims 9to 11, characterized in that the refrigerant temperature relative to thecompressor (14) is the refrigerant temperature (T₃₆) at the outlet ofthe compressor.
 15. The air conditioning unit as claimed in claim 14,characterized in that it includes a probe (36) placed at the outlet ofthe compressor (14) for measuring the refrigerant temperature (T₃₆) atthe outlet of the compressor.